An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures
The article contains a study of methods for solving integral equations in the context of acoustic problems. The methodology considered is applied to describe acoustic wave propagation and scattering. Efficient discretization methods are used together with iterative methods to solve the operator equa...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/6/789 |
| _version_ | 1797240154457374720 |
|---|---|
| author | Alexander B. Samokhin Ivan A. Yurchenkov |
| author_facet | Alexander B. Samokhin Ivan A. Yurchenkov |
| author_sort | Alexander B. Samokhin |
| collection | DOAJ |
| description | The article contains a study of methods for solving integral equations in the context of acoustic problems. The methodology considered is applied to describe acoustic wave propagation and scattering. Efficient discretization methods are used together with iterative methods to solve the operator equations, including an apparatus for fast multiplication of the resulting post-discretization Toeplitz matrices by a vector using the fast Fourier transform. The theoretical analysis of the proposed numerical algorithm demonstrates its efficiency in terms of the required number of arithmetic operations and the memory footprint of the computing system. The presented numerical simulation demonstrates the possibility of solving the problem of acoustic wave propagation in transparent media using the proposed methods. A visualization of the obtained solutions for a practical problem with a high level of discretization of the solution volume domain is also presented. |
| first_indexed | 2024-04-24T18:02:55Z |
| format | Article |
| id | doaj.art-b021b68f78704ffc85cbfa85833c4b58 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:55Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b021b68f78704ffc85cbfa85833c4b582024-03-27T13:52:55ZengMDPI AGMathematics2227-73902024-03-0112678910.3390/math12060789An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent StructuresAlexander B. Samokhin0Ivan A. Yurchenkov1Institute of Information Technologies, Federal State Budget Educational Institution of Higher Education, MIREA—Russian Technological University, 78 Vernadsky Avenue, 119454 Moscow, RussiaInstitute of Information Technologies, Federal State Budget Educational Institution of Higher Education, MIREA—Russian Technological University, 78 Vernadsky Avenue, 119454 Moscow, RussiaThe article contains a study of methods for solving integral equations in the context of acoustic problems. The methodology considered is applied to describe acoustic wave propagation and scattering. Efficient discretization methods are used together with iterative methods to solve the operator equations, including an apparatus for fast multiplication of the resulting post-discretization Toeplitz matrices by a vector using the fast Fourier transform. The theoretical analysis of the proposed numerical algorithm demonstrates its efficiency in terms of the required number of arithmetic operations and the memory footprint of the computing system. The presented numerical simulation demonstrates the possibility of solving the problem of acoustic wave propagation in transparent media using the proposed methods. A visualization of the obtained solutions for a practical problem with a high level of discretization of the solution volume domain is also presented.https://www.mdpi.com/2227-7390/12/6/789integral equationscollocation methoditerative methodmodified gradient descent methodfast Fourier transform |
| spellingShingle | Alexander B. Samokhin Ivan A. Yurchenkov An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures Mathematics integral equations collocation method iterative method modified gradient descent method fast Fourier transform |
| title | An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures |
| title_full | An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures |
| title_fullStr | An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures |
| title_full_unstemmed | An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures |
| title_short | An Efficient Method for Solving Problems of Acoustic Scattering on Three-Dimensional Transparent Structures |
| title_sort | efficient method for solving problems of acoustic scattering on three dimensional transparent structures |
| topic | integral equations collocation method iterative method modified gradient descent method fast Fourier transform |
| url | https://www.mdpi.com/2227-7390/12/6/789 |
| work_keys_str_mv | AT alexanderbsamokhin anefficientmethodforsolvingproblemsofacousticscatteringonthreedimensionaltransparentstructures AT ivanayurchenkov anefficientmethodforsolvingproblemsofacousticscatteringonthreedimensionaltransparentstructures AT alexanderbsamokhin efficientmethodforsolvingproblemsofacousticscatteringonthreedimensionaltransparentstructures AT ivanayurchenkov efficientmethodforsolvingproblemsofacousticscatteringonthreedimensionaltransparentstructures |